Fluid-beam interaction: Capturing the effect of embedded slender bodies on global fluid flow and vice versa

Abstract

This work addresses research questions arising from the application of geometrically exact beam theory in the context of fluid-structure interaction (FSI). Geometrically exact beam theory has proven to be a computationally efficient way to model the behavior of slender structures while leading to rather well-posed problem descriptions. In particular, we propose a mixed-dimensional embedded finite element approach for the coupling of one-dimensional geometrically exact beam equations to a three-dimensional background fluid mesh, referred to as fluid-beam interaction (FBI) in analogy to the well-established notion of FSI. Here, the fluid is described by the incompressible isothermal Navier-Stokes equations for Newtonian fluids. In particular, we present algorithmic aspects regarding the solution of the resulting one-way coupling schemes and, through selected numerical examples, analyze their spatial convergence behavior as well as their suitability not only as stand-alone methods but also for an extension to a full two-way coupling scheme.

References in corpus (2)

• An immersed boundary method for the fluid-structure interaction of slender flexible structures in viscous fluid
• Finite Element Formulations for Beam-to-Solid Interaction -- From Embedded Fibers Towards Contact

Cited by in corpus (4)

• Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes
• An approximate block factorization preconditioner for mixed-dimensional beam-solid interaction
• A consistent mixed-dimensional coupling approach for 1D Cosserat beams and 2D surfaces in 3D space
• Linking discrete and continuum diffusion models: Well-posedness and stable finite element discretizations